~In a bowl, toss the onion with 1 tablespoon of the four and 1/4 teaspoon salt. Heat 1.5 tablespoons of the oil in a large skillet over medium-high heat. Cook the onion, stirring, until golden brown, 1 to 2 minutes; transfer to a plate.~Wipe out the skillet and heat the remaining tablespoon of oil over medium-high heat. cook mushrooms, stirring, until tender, 5 to 6 minutes.~Reduce heat to medium. Sprinkle the remaining tablespoon of flour over the mushrooms and cook, stirring, for 1 minute. Add the milk and 1/4 teaspoon each salt and pepper. Simmer, stirring , until mixture begins to thicken, 1 to 2 minutes. Add green beans and cook until heated through, 3 to 4 minutes. Top with the onions.